In this article you will find a collection of riddles. They are all either very well known or extremely easy. Enjoy!
Cutting the Cake
How can you cut a circular cake to eight even pieces with 3 cuts? What is the maximum number of pieces possible with 4 cuts?
When considering the extra-credit of the 23 and 2000 riddle, I thought of an additional interesting problem.
Let N be a positive integer. A partition of N into m parts (an m-partition of N) is a multiset of m positive integers, such that their sum equals N. A multiset is a set which may contain repeated elements.
You are given 23 whole numbers, not necessarily distinct, in a row.
You cannot change the order of the numbers.
Prove that there exists an arrangement of the symbols ’+’, ‘×’, ‘(‘ and ‘)’ in-between the 23 numbers, such that the final result is a valid formula, whose evaluated value equals 0 mod 2000.
When I started yaniv.leviathanonline.com, I declared it to be a site about “Mathematics and Hacking”. As of now, most of its content is Mathematical. I thought it was time for a little change…
There are 100 seats in an airplane.
There are 99 male passangers with reserved seats and one female passager that does not have a ticket.
The female passanger enters the plane first, selects a random seat (out of the total 100 seats) and sits in it.
Then the first man enters. If his seat is not taken he sits in it. If it is taken he selects a non-occupied random seat in the plane and sits there.
The rest of the men enters and does the same – each of them first tries to take his own seat (if it is available) and otherwise sits in a random non-occupied seat.
There are 100 coins on the table. 90 of the coins have their Heads face up, the other 10 have their Tails face up. Your task is to split the coins into two groups, such that both groups contain the same number of coins with their Heads face up. You are even allowed to flip the coins…
This one is a riddle of my own invention. It gives a very good counter-example to something we tend to take for granted. Do not be discouraged – I posed it to one of my smartest professors and he did not find the answer! (at least not in the first five minutes…).
The riddle requires some knowledge of Topology and Real-Analysis. For those of you lacking it, all the relevant definitions are included at the end (I recommend skimming through them before reading the riddle itself).
A couple of years ago I was very interested in visualizing objects of more than three dimensions. I reasoned that if I stared at such objects for long enough time, I was bound to get a good intuition on how they look.
But how can one see objects of more than three spatial dimensions?
Our goal in this post will be to render an object residing in a coordinate system of arbitrary dimensions on a 2D computer screen. We will try to do this in such a way as to lose as little information as possible on the structure of the object, while maintaining its 2D description as simple as possible (so that indeed, we will get some form of intuition on the shape of the object).
This is the first riddle I post in my site that I haven’t yet solved.
Because of this, I give it the “very hard” icon. It may turn out to be easy – do not be intimidated!
Hi everyone!
As you may have noticed, yaniv.leviathanonline.com has not been updated for a while (exactly one month, pour être précis). This was largely due to my intense exam period.